Modern controllers generally sense the operation of a system, compare that against a desired behavior, compute corrective actions based on a model of the system's response to external inputs, and actuate the system to effect the desired change. Generally, the key issues in designing control logic are ensuring that the dynamics of the closed loop system are stable and have the desired behaviors, such as good disturbance rejection, fast responsiveness, and others. These properties are established using a variety of modeling and analysis techniques that capture the essential physics of the system and permit the exploration of possible behaviors in the presence of uncertainty, noise and component failures. However, measurement noise and other uncertainties may corrupt the information about the process variables that sensors deliver. Additionally, the dynamics of the closed loop system as expressed in control allocation or other control mapping functions may lead to extreme sensitivities at certain operating points, making a process difficult to control.
Often the impacts of uncertainties or excessive sensitivity are dealt with by designing inviolable thresholds well within a given system's available operating envelope when necessary, or simply living with the impact of the uncertainties when such reliance can be safely afforded. These standard approaches act to reduces the size of operational envelopes and degrade performance, and often require oversized systems since only a fraction of the system's true capability is utilized during operation. Alternatively, in some cases and when such reliance may be safely afforded, the impact of uncertainties on the performance of a system may be simply accepted as part of the overall process, and the uncertainty is treated as a limitation on the ultimate fidelity of the system.
It would be advantageous to provide a closed-loop control system allowing alternative and more beneficial treatment of various high sensitivity operating points and measurement uncertainties. Such a control system would allow for expanded operation within inherent operating envelopes and improve the overall performance of various systems. Correspondingly, disclosed herein is a closed-loop controller for a controlled system which improves system performance by treating identified system state input parameters and system output parameters as a collection of possibly uncertain points identified by utilizing a statistical distribution parameterized by a mean and a variance and/or covariance denoted herein as a (μ,σ2) distribution around the identified parameter. The controlled system is described by a control effectiveness function relating a desired system response to the system state input and system output parameters, and a control allocator within the closed-loop controller utilizes the control effectiveness function to minimize an error function, where the errors arise through use of the use of the (μ,σ2) distributed points within the control effectiveness function. The closed-loop controller may be utilized by any controlled system having a control effectiveness function in order to increase available performance.
These and other objects, aspects, and advantages of the present disclosure will become better understood with reference to the accompanying description and claims.